AI 中文总结
研究大量粒子壳上分裂函数，基于Soper-Weinberg共线旋量提出构造形式，推导标准模型粒子分裂函数集，建立匹配字典，通过递归关系获更高点函数，为对撞机物理和部分子喷注发展提供计算工具。
AI 中文摘要
共线分裂函数控制着高能对撞机中的部分子演化、部分子喷注和重整化。虽然壳上旋量-螺旋度方法已成功得出无质量QCD分裂函数，但对于大量粒子的完整壳上构造，系统纳入有限质量效应的研究较少。我们基于Soper-Weinberg共线旋量提出了一种用于大量共线分裂函数的壳上构造形式，其变换性质源于庞加莱群的光前伽利略子群。相对于固定的类光矢量\(n\)和\(\bar n\)分解大量动量和旋量，使得在\(m<p_T\ll p_+\)的对齐区域中的展开明显。领先阶结构与无质量三点振幅匹配，而沿\(\bar n\)的额外希格斯动量探测次领先旋量分量并将它们与无质量四点振幅相关联。我们推导了所有标准模型粒子的完整领先和次领先大量分裂函数集，并在三点和四点水平上建立了无质量和大量耦合系数之间的系统匹配字典。更高点分裂函数通过具有通用替换规则的递归自举关系获得，这是伽利略对称性的结果。这个构造框架自然地扩展到有效场论算符和更高的微扰阶数，为精确对撞机物理和部分子喷注发展提供了一个灵活的计算工具。
英文摘要
Collinear splitting functions govern parton evolution, parton showers, and resummation at high-energy colliders. While on-shell spinor-helicity methods have successfully yielded massless QCD splitting functions, a complete on-shell construction for massive particles, systematically incorporating finite-mass effects, is less developed. We present an on-shell constructive formalism for massive collinear splitting functions based on Soper-Weinberg collinear spinors, whose transformation properties follow from a light-front Galilean subgroup of the Poincaré group. Decomposing massive momenta and spinors with respect to fixed lightlike vectors $n$ and $\bar n$ makes the expansion in the alignment regime $m<p_T\ll p_+$ manifest. The leading-order structures are matched to massless three-point amplitudes, while an additional Higgs momentum along $\bar n$ probes the subleading spinor components and relates them to massless four-point amplitudes. We derive the complete set of leading and subleading massive splitting functions for all Standard Model particles and establish a systematic matching dictionary between massless and massive coupling coefficients at both the three- and four-point levels. Higher-point splitting functions are obtained through the recursive bootstrap relation with a universal substitution rule as a consequence of the Galilean symmetry. This constructive framework extends naturally to effective field theory operators and higher perturbative orders, providing a flexible computational tool for precision collider physics and parton shower development.
Comments57 pages, 11 figures, 4 tables, reference updated
